The best polynomial bounds for the number of triangles in a simple arrangement of n pseudo-lines

Details The best polynomial bounds for the number of triangles in a simple arrangement of n pseudo-lines The best polynomial bounds for the number of triangles in a simple arrangement of n pseudo-lines

2008-01-18

arxiv.org/abs/0801.2845v2

Mathematics

Combinatorics

12 pages, 7 figures

Scientific paper

It is well-known that affine (respectively projective) simple arrangements of
n pseudo-lines may have at most n(n-2)/3 (respectively n(n-1)/3) triangles.
However, these bounds are reached for only some values of n (mod 6). We provide
the best polynomial bound for the affine and the projective case, and for each
value of n (mod 6).

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